In this section, we will be mainly concerned about the existence of
gluings, as they will be of use in the construction of the cccc
version of a locally ccc MSN in Section . This turns
out to depend both on the domain and the target space. In case where
\((Y, {B})\)  is the real line equipped with its Borel
\(\sigma \) -algebra \((\mathbb {R}, {B}(\mathbb {R}))\) , we can glue measurable functions
together if \((X, {A}, {N})\)  is localizable. In fact, this
important property is a characterization of localizability. The
interested reader may find a proof of this classical result
expressed in the language of MSNs in [1]}. Only the measurable structure of \((\mathbb {R},{B}(\mathbb {R}))\)  is involved, thus, the result holds in the more general case where
\((Y, {B})\)  is a standard Borel space, see [2]}.
